Two-sample test for sparse high-dimensional multinomial distributions

Amanda Plunkett () and Junyong Park ()
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Amanda Plunkett: Department of Defense
Junyong Park: University of Maryland Baltimore County

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2019, vol. 28, issue 3, No 12, 804-826

Abstract: Abstract In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical Chi-square test may have some drawbacks in this case since many of cell counts may be zero or may not be large enough. We propose a new test and show its asymptotic normality and the asymptotic power function. Based on the asymptotic power function, we present an application of our result to a neighborhood-type test which has been previously studied, especially for the case of fairly small p values. To compare the proposed test with existing tests, we provide numerical studies including simulations and real data examples.

Keywords: Two-sample test; High-dimensional multinomial; Sparseness; 62H15; 62E20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11749-018-0600-8

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